Invariant polynomial
In mathematics, an invariant polynomial is a polynomial that is invariant under a group acting on a vector space . Therefore is a -invariant polynomial if
for all and .
Cases of particular importance are for Γ a finite group (in the theory of Molien series, in particular), a compact group, a Lie group or algebraic group. For a basis-independent definition of 'polynomial' nothing is lost by referring to the symmetric powers of the given linear representation of Γ.
References
- This article incorporates material from Invariant polynomial on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.
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